I just finished reading Polly Evans' It's Not About The Tapas. She cycled 1000 miles in Spain and little of it was leisurely. Very funny book, if you are interested. My local library carries it, but I expect there may be an ebook.
Spain is very hilly, and the Spaniards take there bicycling seriously. Even the cities are hilly, so save your bike vacations for the Netherlands. Lovely flat, made for bikes, country.
Would you be interested in a day tour for nature? I am a bird wstcher and have arranged a day trip to Donana NP from Seville. It is a private tour but it is per vehicle not per person, so pricing may not be as bad as a Viator type tour. Many birding companies also do hiking, nature viewing days. There is also one out of Antequera. There is some rugged country there that may be of interest. El Torcal de Antequera Nature Reserve is in limestone Karst landscape. There is a visitor's centre so there may be a website with maps. Keep in mind that two years ago, late September in Seville had temps close to 100F though last year the did occasionally drop to low 80s, so check your weather history data before olanning a day hiking in the hills